A non-compromising method for optimizing multi-objective problems

Abstract Multi-objective optimization often entails the concurrent optimization of multiple objectives, which may exhibit conflicts. In many engineering application fields and machine learning algorithms, when determining the final solution, there is a need for trade-offs among different optimization objectives using weight parameters. Here we propose a novel methodology, called Rise-Dimension Screen(RDS), to screen the optimal solution of multi-objective optimization problems from Pareto Front, without the need for compromising between different optimization objectives. We elevate the deterministic numerical values of design variables (0-dimensional space) to a probability density function (1-dimensional space) based on historical data, thereby raising the corresponding constraint conditions to a high-dimensional space. We evaluate their quality by calculating the probability characteristics of different non-inferior solutions satisfying the high-dimensional space constraints, and define the non-inferior solution with the highest probability of meeting the constraint conditions as the final decision solution.